Resumen de Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts

Shuang Chen, Yuanjin Ren

• Differential equation modelling was earlier used to discover better and understand various biological phenomena and socialproblems. We hope to understand the stability of the system and the Hopf bifurcation based on the characteristic roots ofthe linear system. Because group competitive sports require participants to have certain competitive skills, those who donot have sports skills but want to develop into activities must receive training and specific training. Therefore, based onthe research background, the article proposes a time-lag group competitive martial arts activity model with a time lageffect. Through delay differential equation theory and Hopf bifurcation theory, the stability of the equilibrium point andthe existence of periodic solutions generated by the Hopf bifurcation caused by the ‘instability’ of the equilibrium pointare discussed. Finally, the theoretical results are simulated and verified with the help of MATLAB software